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The <a href="https://wiki.jenkins-ci.org/display/JENKINS/Github+Plugin">github-plugin</a> has a web hook trigger that can be used to notify Jenkins when a push has occurred and that a build should also happen. <br/> By enabling this permission you grant anonymous external READ access to the <b>/github-webhook</b> URL so that the request can be received.
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The <a href="https://wiki.jenkins-ci.org/display/JENKINS/Github+Plugin">github-plugin</a> checks that a change has actually occurred so this should be safe to enable.

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